%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV003-3 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:34:15 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 128
% Number of leaves : 55
% Syntax : Number of formulae : 288 ( 15 unt; 0 def)
% Number of atoms : 873 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 804 ( 219 ~; 585 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 23 ( 22 usr; 23 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause_1A,axiom,
( a
| a11 ),
file('theBenchmark.p',clause_1A) ).
cnf(c_1,plain,
( a
| a11 ),
inference(clausify,[status(thm)],[clause_1A]) ).
fof(clause_1B,axiom,
( b
| a11 ),
file('theBenchmark.p',clause_1B) ).
cnf(c_2,plain,
( b
| a11 ),
inference(clausify,[status(thm)],[clause_1B]) ).
fof(clause_1C,axiom,
( ~ b
| ~ a
| ~ a11 ),
file('theBenchmark.p',clause_1C) ).
cnf(c_3,plain,
( ~ b
| ~ a
| ~ a11 ),
inference(clausify,[status(thm)],[clause_1C]) ).
fof(clause_2A,axiom,
( a
| a12 ),
file('theBenchmark.p',clause_2A) ).
cnf(c_4,plain,
( a
| a12 ),
inference(clausify,[status(thm)],[clause_2A]) ).
fof(clause_2B,axiom,
( a11
| a12 ),
file('theBenchmark.p',clause_2B) ).
cnf(c_5,plain,
( a11
| a12 ),
inference(clausify,[status(thm)],[clause_2B]) ).
fof(clause_2C,axiom,
( ~ a11
| ~ a
| ~ a12 ),
file('theBenchmark.p',clause_2C) ).
cnf(c_6,plain,
( ~ a11
| ~ a
| ~ a12 ),
inference(clausify,[status(thm)],[clause_2C]) ).
fof(clause_3A,axiom,
( b
| a13 ),
file('theBenchmark.p',clause_3A) ).
cnf(c_7,plain,
( b
| a13 ),
inference(clausify,[status(thm)],[clause_3A]) ).
fof(clause_3B,axiom,
( a11
| a13 ),
file('theBenchmark.p',clause_3B) ).
cnf(c_8,plain,
( a11
| a13 ),
inference(clausify,[status(thm)],[clause_3B]) ).
fof(clause_3C,axiom,
( ~ a11
| ~ b
| ~ a13 ),
file('theBenchmark.p',clause_3C) ).
cnf(c_9,plain,
( ~ a11
| ~ b
| ~ a13 ),
inference(clausify,[status(thm)],[clause_3C]) ).
fof(clause_4A,axiom,
( a12
| a14 ),
file('theBenchmark.p',clause_4A) ).
cnf(c_10,plain,
( a12
| a14 ),
inference(clausify,[status(thm)],[clause_4A]) ).
fof(clause_4B,axiom,
( a13
| a14 ),
file('theBenchmark.p',clause_4B) ).
cnf(c_11,plain,
( a13
| a14 ),
inference(clausify,[status(thm)],[clause_4B]) ).
fof(clause_4C,axiom,
( ~ a13
| ~ a12
| ~ a14 ),
file('theBenchmark.p',clause_4C) ).
cnf(c_12,plain,
( ~ a13
| ~ a12
| ~ a14 ),
inference(clausify,[status(thm)],[clause_4C]) ).
fof(clause_5A,axiom,
( a14
| a15 ),
file('theBenchmark.p',clause_5A) ).
cnf(c_13,plain,
( a14
| a15 ),
inference(clausify,[status(thm)],[clause_5A]) ).
fof(clause_5B,axiom,
( cI
| a15 ),
file('theBenchmark.p',clause_5B) ).
cnf(c_14,plain,
( cI
| a15 ),
inference(clausify,[status(thm)],[clause_5B]) ).
fof(clause_5C,axiom,
( ~ cI
| ~ a14
| ~ a15 ),
file('theBenchmark.p',clause_5C) ).
cnf(c_15,plain,
( ~ cI
| ~ a14
| ~ a15 ),
inference(clausify,[status(thm)],[clause_5C]) ).
fof(clause_6A,axiom,
( a14
| a16 ),
file('theBenchmark.p',clause_6A) ).
cnf(c_16,plain,
( a14
| a16 ),
inference(clausify,[status(thm)],[clause_6A]) ).
fof(clause_6B,axiom,
( a15
| a16 ),
file('theBenchmark.p',clause_6B) ).
cnf(c_17,plain,
( a15
| a16 ),
inference(clausify,[status(thm)],[clause_6B]) ).
fof(clause_6C,axiom,
( ~ a15
| ~ a14
| ~ a16 ),
file('theBenchmark.p',clause_6C) ).
cnf(c_18,plain,
( ~ a15
| ~ a14
| ~ a16 ),
inference(clausify,[status(thm)],[clause_6C]) ).
fof(clause_7A,axiom,
( a15
| a17 ),
file('theBenchmark.p',clause_7A) ).
cnf(c_19,plain,
( a15
| a17 ),
inference(clausify,[status(thm)],[clause_7A]) ).
fof(clause_7B,axiom,
( cI
| a17 ),
file('theBenchmark.p',clause_7B) ).
cnf(c_20,plain,
( cI
| a17 ),
inference(clausify,[status(thm)],[clause_7B]) ).
fof(clause_7C,axiom,
( ~ cI
| ~ a15
| ~ a17 ),
file('theBenchmark.p',clause_7C) ).
cnf(c_21,plain,
( ~ cI
| ~ a15
| ~ a17 ),
inference(clausify,[status(thm)],[clause_7C]) ).
fof(clause_8A,axiom,
( a16
| s1 ),
file('theBenchmark.p',clause_8A) ).
cnf(c_22,plain,
( a16
| s1 ),
inference(clausify,[status(thm)],[clause_8A]) ).
fof(clause_8B,axiom,
( a17
| s1 ),
file('theBenchmark.p',clause_8B) ).
cnf(c_23,plain,
( a17
| s1 ),
inference(clausify,[status(thm)],[clause_8B]) ).
fof(clause_8C,axiom,
( ~ a17
| ~ a16
| ~ s1 ),
file('theBenchmark.p',clause_8C) ).
cnf(c_24,plain,
( ~ a17
| ~ a16
| ~ s1 ),
inference(clausify,[status(thm)],[clause_8C]) ).
fof(clause_9A,axiom,
( a15
| c1 ),
file('theBenchmark.p',clause_9A) ).
cnf(c_25,plain,
( a15
| c1 ),
inference(clausify,[status(thm)],[clause_9A]) ).
fof(clause_9B,axiom,
( a11
| c1 ),
file('theBenchmark.p',clause_9B) ).
cnf(c_26,plain,
( a11
| c1 ),
inference(clausify,[status(thm)],[clause_9B]) ).
fof(clause_9C,axiom,
( ~ a11
| ~ a15
| ~ c1 ),
file('theBenchmark.p',clause_9C) ).
cnf(c_27,plain,
( ~ a11
| ~ a15
| ~ c1 ),
inference(clausify,[status(thm)],[clause_9C]) ).
fof(clause_10A,axiom,
( ~ b
| a
| a21 ),
file('theBenchmark.p',clause_10A) ).
cnf(c_28,plain,
( ~ b
| a
| a21 ),
inference(clausify,[status(thm)],[clause_10A]) ).
fof(clause_10B,axiom,
( b
| ~ a
| a21 ),
file('theBenchmark.p',clause_10B) ).
cnf(c_29,plain,
( b
| ~ a
| a21 ),
inference(clausify,[status(thm)],[clause_10B]) ).
fof(clause_10C,axiom,
( b
| a
| ~ a21 ),
file('theBenchmark.p',clause_10C) ).
cnf(c_30,plain,
( b
| a
| ~ a21 ),
inference(clausify,[status(thm)],[clause_10C]) ).
fof(clause_10D,axiom,
( ~ b
| ~ a
| ~ a21 ),
file('theBenchmark.p',clause_10D) ).
cnf(c_31,plain,
( ~ b
| ~ a
| ~ a21 ),
inference(clausify,[status(thm)],[clause_10D]) ).
fof(clause_11A,axiom,
( cI
| ~ a22 ),
file('theBenchmark.p',clause_11A) ).
cnf(c_32,plain,
( cI
| ~ a22 ),
inference(clausify,[status(thm)],[clause_11A]) ).
fof(clause_11B,axiom,
( a23
| ~ a22 ),
file('theBenchmark.p',clause_11B) ).
cnf(c_33,plain,
( a23
| ~ a22 ),
inference(clausify,[status(thm)],[clause_11B]) ).
fof(clause_11C,axiom,
( ~ a23
| ~ cI
| a22 ),
file('theBenchmark.p',clause_11C) ).
cnf(c_34,plain,
( ~ a23
| ~ cI
| a22 ),
inference(clausify,[status(thm)],[clause_11C]) ).
fof(clause_12A,axiom,
( ~ a
| a23 ),
file('theBenchmark.p',clause_12A) ).
cnf(c_35,plain,
( ~ a
| a23 ),
inference(clausify,[status(thm)],[clause_12A]) ).
fof(clause_12B,axiom,
( ~ b
| a23 ),
file('theBenchmark.p',clause_12B) ).
cnf(c_36,plain,
( ~ b
| a23 ),
inference(clausify,[status(thm)],[clause_12B]) ).
fof(clause_12C,axiom,
( b
| a
| ~ a23 ),
file('theBenchmark.p',clause_12C) ).
cnf(c_37,plain,
( b
| a
| ~ a23 ),
inference(clausify,[status(thm)],[clause_12C]) ).
fof(clause_13A,axiom,
( cI
| a24 ),
file('theBenchmark.p',clause_13A) ).
cnf(c_38,plain,
( cI
| a24 ),
inference(clausify,[status(thm)],[clause_13A]) ).
fof(clause_14A,axiom,
( a
| ~ a25 ),
file('theBenchmark.p',clause_14A) ).
cnf(c_40,plain,
( a
| ~ a25 ),
inference(clausify,[status(thm)],[clause_14A]) ).
fof(clause_14B,axiom,
( b
| ~ a25 ),
file('theBenchmark.p',clause_14B) ).
cnf(c_41,plain,
( b
| ~ a25 ),
inference(clausify,[status(thm)],[clause_14B]) ).
fof(clause_14C,axiom,
( ~ b
| ~ a
| a25 ),
file('theBenchmark.p',clause_14C) ).
cnf(c_42,plain,
( ~ b
| ~ a
| a25 ),
inference(clausify,[status(thm)],[clause_14C]) ).
fof(clause_15B,axiom,
( a25
| ~ a26 ),
file('theBenchmark.p',clause_15B) ).
cnf(c_44,plain,
( a25
| ~ a26 ),
inference(clausify,[status(thm)],[clause_15B]) ).
fof(clause_15C,axiom,
( ~ a25
| ~ a24
| a26 ),
file('theBenchmark.p',clause_15C) ).
cnf(c_45,plain,
( ~ a25
| ~ a24
| a26 ),
inference(clausify,[status(thm)],[clause_15C]) ).
fof(clause_16A,axiom,
( ~ a21
| cI
| s2 ),
file('theBenchmark.p',clause_16A) ).
cnf(c_46,plain,
( ~ a21
| cI
| s2 ),
inference(clausify,[status(thm)],[clause_16A]) ).
fof(clause_16B,axiom,
( a21
| ~ cI
| s2 ),
file('theBenchmark.p',clause_16B) ).
cnf(c_47,plain,
( a21
| ~ cI
| s2 ),
inference(clausify,[status(thm)],[clause_16B]) ).
fof(clause_16C,axiom,
( a21
| cI
| ~ s2 ),
file('theBenchmark.p',clause_16C) ).
cnf(c_48,plain,
( a21
| cI
| ~ s2 ),
inference(clausify,[status(thm)],[clause_16C]) ).
fof(clause_16D,axiom,
( ~ a21
| ~ cI
| ~ s2 ),
file('theBenchmark.p',clause_16D) ).
cnf(c_49,plain,
( ~ a21
| ~ cI
| ~ s2 ),
inference(clausify,[status(thm)],[clause_16D]) ).
fof(clause_17A,axiom,
( ~ a22
| c2 ),
file('theBenchmark.p',clause_17A) ).
cnf(c_50,plain,
( ~ a22
| c2 ),
inference(clausify,[status(thm)],[clause_17A]) ).
fof(clause_17B,axiom,
( ~ a26
| c2 ),
file('theBenchmark.p',clause_17B) ).
cnf(c_51,plain,
( ~ a26
| c2 ),
inference(clausify,[status(thm)],[clause_17B]) ).
fof(clause_17C,axiom,
( a26
| a22
| ~ c2 ),
file('theBenchmark.p',clause_17C) ).
cnf(c_52,plain,
( a26
| a22
| ~ c2 ),
inference(clausify,[status(thm)],[clause_17C]) ).
fof(clause_18C,axiom,
( s2
| s1
| ~ conjline18 ),
file('theBenchmark.p',clause_18C) ).
cnf(c_55,plain,
( s2
| s1
| ~ conjline18 ),
inference(clausify,[status(thm)],[clause_18C]) ).
fof(clause_18D,axiom,
( ~ s2
| ~ s1
| ~ conjline18 ),
file('theBenchmark.p',clause_18D) ).
cnf(c_56,plain,
( ~ s2
| ~ s1
| ~ conjline18 ),
inference(clausify,[status(thm)],[clause_18D]) ).
fof(clause_19C,axiom,
( c2
| c1
| ~ conjline19 ),
file('theBenchmark.p',clause_19C) ).
cnf(c_59,plain,
( c2
| c1
| ~ conjline19 ),
inference(clausify,[status(thm)],[clause_19C]) ).
fof(clause_19D,axiom,
( ~ c2
| ~ c1
| ~ conjline19 ),
file('theBenchmark.p',clause_19D) ).
cnf(c_60,plain,
( ~ c2
| ~ c1
| ~ conjline19 ),
inference(clausify,[status(thm)],[clause_19D]) ).
fof(clause_20,axiom,
( conjline19
| conjline18 ),
file('theBenchmark.p',clause_20) ).
cnf(c_61,plain,
( conjline19
| conjline18 ),
inference(clausify,[status(thm)],[clause_20]) ).
cnf(c_62,plain,
( ~ a11
| ~ a
| a14 ),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_63,plain,
( ~ a11
| ~ b
| a14 ),
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_64,plain,
( a11
| ~ a12
| ~ a14 ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_65,plain,
( b
| ~ a12
| ~ a14 ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_66,plain,
( ~ a15
| ~ a14
| s1 ),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_67,plain,
( ~ cI
| ~ a15
| s1 ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_68,plain,
( cI
| ~ a16
| ~ s1 ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_69,plain,
( a15
| ~ a16
| ~ s1 ),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_70,plain,
( cI
| ~ a25
| a26 ),
inference(resolve,[status(thm)],[c_45,c_38]) ).
cnf(c_73,plain,
( ~ c2
| ~ c1
| conjline18 ),
inference(resolve,[status(thm)],[c_61,c_60]) ).
cnf(c_74,plain,
( c2
| c1
| conjline18 ),
inference(resolve,[status(thm)],[c_61,c_59]) ).
cnf(c_75,plain,
( b
| ~ a
| a14 ),
inference(resolve,[status(thm)],[c_62,c_2]) ).
cnf(c_76,plain,
( a
| ~ b
| a14 ),
inference(resolve,[status(thm)],[c_63,c_1]) ).
cnf(c_225,plain,
( a11
| a11
| ~ a14 ),
inference(resolve,[status(thm)],[c_64,c_5]) ).
cnf(c_77,plain,
( a11
| ~ a14 ),
inference(copy,[status(thm)],[c_225]) ).
cnf(c_78,plain,
( a15
| a11 ),
inference(resolve,[status(thm)],[c_77,c_13]) ).
cnf(c_79,plain,
( a
| b
| ~ a14 ),
inference(resolve,[status(thm)],[c_65,c_4]) ).
cnf(c_80,plain,
( a11
| ~ cI
| s1 ),
inference(resolve,[status(thm)],[c_67,c_78]) ).
cnf(c_81,plain,
( a14
| cI
| ~ s1 ),
inference(resolve,[status(thm)],[c_68,c_16]) ).
cnf(c_226,plain,
( a15
| a15
| ~ s1 ),
inference(resolve,[status(thm)],[c_69,c_17]) ).
cnf(c_82,plain,
( a15
| ~ s1 ),
inference(copy,[status(thm)],[c_226]) ).
cnf(c_83,plain,
( a11
| ~ c2
| conjline18 ),
inference(resolve,[status(thm)],[c_73,c_26]) ).
cnf(c_84,plain,
( a15
| ~ c2
| conjline18 ),
inference(resolve,[status(thm)],[c_73,c_25]) ).
cnf(c_85,plain,
( ~ s2
| ~ s1
| c2
| c1 ),
inference(resolve,[status(thm)],[c_74,c_56]) ).
cnf(c_86,plain,
( s2
| s1
| c2
| c1 ),
inference(resolve,[status(thm)],[c_74,c_55]) ).
cnf(c_87,plain,
( a15
| a
| b ),
inference(resolve,[status(thm)],[c_79,c_13]) ).
cnf(c_88,plain,
( ~ cI
| s1
| a
| b ),
inference(resolve,[status(thm)],[c_87,c_67]) ).
cnf(c_89,plain,
( a14
| cI
| s2
| c2
| c1 ),
inference(resolve,[status(thm)],[c_86,c_81]) ).
cnf(c_90,plain,
( a
| b
| cI
| s2
| c2
| c1 ),
inference(resolve,[status(thm)],[c_89,c_79]) ).
cnf(c_92,plain,
( ~ a11
| ~ a15
| a
| b
| cI
| s2
| c2 ),
inference(resolve,[status(thm)],[c_90,c_27]) ).
cnf(c_227,plain,
( a
| b
| ~ a11
| a
| b
| cI
| s2
| c2 ),
inference(resolve,[status(thm)],[c_92,c_87]) ).
cnf(c_228,plain,
( a
| ~ a11
| a
| b
| cI
| s2
| c2 ),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_93,plain,
( ~ a11
| a
| b
| cI
| s2
| c2 ),
inference(copy,[status(thm)],[c_228]) ).
cnf(c_229,plain,
( b
| a
| b
| cI
| s2
| c2 ),
inference(resolve,[status(thm)],[c_93,c_2]) ).
cnf(c_94,plain,
( a
| b
| cI
| s2
| c2 ),
inference(copy,[status(thm)],[c_229]) ).
cnf(c_230,plain,
( a21
| cI
| a
| b
| cI
| c2 ),
inference(resolve,[status(thm)],[c_94,c_48]) ).
cnf(c_96,plain,
( a21
| a
| b
| cI
| c2 ),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_98,plain,
( a26
| a22
| a21
| a
| b
| cI ),
inference(resolve,[status(thm)],[c_96,c_52]) ).
cnf(c_99,plain,
( a25
| a22
| a21
| a
| b
| cI ),
inference(resolve,[status(thm)],[c_98,c_44]) ).
cnf(c_231,plain,
( b
| a22
| a21
| a
| b
| cI ),
inference(resolve,[status(thm)],[c_99,c_41]) ).
cnf(c_100,plain,
( a22
| a21
| a
| b
| cI ),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_232,plain,
( cI
| a21
| a
| b
| cI ),
inference(resolve,[status(thm)],[c_100,c_32]) ).
cnf(c_102,plain,
( a21
| a
| b
| cI ),
inference(copy,[status(thm)],[c_232]) ).
cnf(c_233,plain,
( b
| a
| a
| b
| cI ),
inference(resolve,[status(thm)],[c_102,c_30]) ).
cnf(c_234,plain,
( b
| a
| b
| cI ),
inference(copy,[status(thm)],[c_233]) ).
cnf(c_104,plain,
( a
| b
| cI ),
inference(copy,[status(thm)],[c_234]) ).
cnf(c_235,plain,
( s1
| a
| b
| a
| b ),
inference(resolve,[status(thm)],[c_104,c_88]) ).
cnf(c_236,plain,
( s1
| a
| a
| b ),
inference(copy,[status(thm)],[c_235]) ).
cnf(c_105,plain,
( s1
| a
| b ),
inference(copy,[status(thm)],[c_236]) ).
cnf(c_106,plain,
( a21
| s2
| a
| b ),
inference(resolve,[status(thm)],[c_104,c_47]) ).
cnf(c_107,plain,
( ~ s2
| c2
| c1
| a
| b ),
inference(resolve,[status(thm)],[c_105,c_85]) ).
cnf(c_237,plain,
( a21
| a
| b
| c2
| c1
| a
| b ),
inference(resolve,[status(thm)],[c_107,c_106]) ).
cnf(c_238,plain,
( a21
| a
| c2
| c1
| a
| b ),
inference(copy,[status(thm)],[c_237]) ).
cnf(c_109,plain,
( a21
| c2
| c1
| a
| b ),
inference(copy,[status(thm)],[c_238]) ).
cnf(c_111,plain,
( ~ a11
| ~ a15
| a21
| c2
| a
| b ),
inference(resolve,[status(thm)],[c_109,c_27]) ).
cnf(c_239,plain,
( a
| b
| ~ a11
| a21
| c2
| a
| b ),
inference(resolve,[status(thm)],[c_111,c_87]) ).
cnf(c_240,plain,
( a
| ~ a11
| a21
| c2
| a
| b ),
inference(copy,[status(thm)],[c_239]) ).
cnf(c_112,plain,
( ~ a11
| a21
| c2
| a
| b ),
inference(copy,[status(thm)],[c_240]) ).
cnf(c_241,plain,
( b
| a21
| c2
| a
| b ),
inference(resolve,[status(thm)],[c_112,c_2]) ).
cnf(c_113,plain,
( a21
| c2
| a
| b ),
inference(copy,[status(thm)],[c_241]) ).
cnf(c_115,plain,
( a26
| a22
| a21
| a
| b ),
inference(resolve,[status(thm)],[c_113,c_52]) ).
cnf(c_116,plain,
( a25
| a22
| a21
| a
| b ),
inference(resolve,[status(thm)],[c_115,c_44]) ).
cnf(c_242,plain,
( b
| a22
| a21
| a
| b ),
inference(resolve,[status(thm)],[c_116,c_41]) ).
cnf(c_118,plain,
( a22
| a21
| a
| b ),
inference(copy,[status(thm)],[c_242]) ).
cnf(c_119,plain,
( a23
| a21
| a
| b ),
inference(resolve,[status(thm)],[c_118,c_33]) ).
cnf(c_243,plain,
( b
| a
| a21
| a
| b ),
inference(resolve,[status(thm)],[c_119,c_37]) ).
cnf(c_244,plain,
( b
| a21
| a
| b ),
inference(copy,[status(thm)],[c_243]) ).
cnf(c_120,plain,
( a21
| a
| b ),
inference(copy,[status(thm)],[c_244]) ).
cnf(c_245,plain,
( b
| a
| a
| b ),
inference(resolve,[status(thm)],[c_120,c_30]) ).
cnf(c_246,plain,
( b
| a
| b ),
inference(copy,[status(thm)],[c_245]) ).
cnf(c_121,plain,
( a
| b ),
inference(copy,[status(thm)],[c_246]) ).
cnf(c_247,plain,
( a
| a14
| a ),
inference(resolve,[status(thm)],[c_121,c_76]) ).
cnf(c_122,plain,
( a14
| a ),
inference(copy,[status(thm)],[c_247]) ).
cnf(c_123,plain,
( a23
| a ),
inference(resolve,[status(thm)],[c_121,c_36]) ).
cnf(c_248,plain,
( a
| a21
| a ),
inference(resolve,[status(thm)],[c_121,c_28]) ).
cnf(c_124,plain,
( a21
| a ),
inference(copy,[status(thm)],[c_248]) ).
cnf(c_125,plain,
( ~ a15
| s1
| a ),
inference(resolve,[status(thm)],[c_122,c_66]) ).
cnf(c_126,plain,
( ~ cI
| ~ a15
| a ),
inference(resolve,[status(thm)],[c_122,c_15]) ).
cnf(c_127,plain,
( ~ cI
| a22
| a ),
inference(resolve,[status(thm)],[c_123,c_34]) ).
cnf(c_128,plain,
( cI
| s2
| a ),
inference(resolve,[status(thm)],[c_124,c_46]) ).
cnf(c_129,plain,
( cI
| s1
| a ),
inference(resolve,[status(thm)],[c_125,c_14]) ).
cnf(c_130,plain,
( ~ s2
| c2
| c1
| cI
| a ),
inference(resolve,[status(thm)],[c_129,c_85]) ).
cnf(c_249,plain,
( cI
| a
| c2
| c1
| cI
| a ),
inference(resolve,[status(thm)],[c_130,c_128]) ).
cnf(c_250,plain,
( cI
| c2
| c1
| cI
| a ),
inference(copy,[status(thm)],[c_249]) ).
cnf(c_131,plain,
( c2
| c1
| cI
| a ),
inference(copy,[status(thm)],[c_250]) ).
cnf(c_133,plain,
( ~ a11
| ~ a15
| c2
| cI
| a ),
inference(resolve,[status(thm)],[c_131,c_27]) ).
cnf(c_251,plain,
( cI
| ~ a11
| c2
| cI
| a ),
inference(resolve,[status(thm)],[c_133,c_14]) ).
cnf(c_134,plain,
( ~ a11
| c2
| cI
| a ),
inference(copy,[status(thm)],[c_251]) ).
cnf(c_252,plain,
( a
| c2
| cI
| a ),
inference(resolve,[status(thm)],[c_134,c_1]) ).
cnf(c_135,plain,
( c2
| cI
| a ),
inference(copy,[status(thm)],[c_252]) ).
cnf(c_137,plain,
( a26
| a22
| cI
| a ),
inference(resolve,[status(thm)],[c_135,c_52]) ).
cnf(c_138,plain,
( a25
| a22
| cI
| a ),
inference(resolve,[status(thm)],[c_137,c_44]) ).
cnf(c_253,plain,
( a
| a22
| cI
| a ),
inference(resolve,[status(thm)],[c_138,c_40]) ).
cnf(c_139,plain,
( a22
| cI
| a ),
inference(copy,[status(thm)],[c_253]) ).
cnf(c_254,plain,
( cI
| cI
| a ),
inference(resolve,[status(thm)],[c_139,c_32]) ).
cnf(c_140,plain,
( cI
| a ),
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
( a22
| a
| a ),
inference(resolve,[status(thm)],[c_140,c_127]) ).
cnf(c_141,plain,
( a22
| a ),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_142,plain,
( c2
| a ),
inference(resolve,[status(thm)],[c_141,c_50]) ).
cnf(c_143,plain,
( a15
| conjline18
| a ),
inference(resolve,[status(thm)],[c_142,c_84]) ).
cnf(c_145,plain,
( s2
| s1
| a15
| a ),
inference(resolve,[status(thm)],[c_143,c_55]) ).
cnf(c_256,plain,
( a15
| s2
| a15
| a ),
inference(resolve,[status(thm)],[c_145,c_82]) ).
cnf(c_146,plain,
( s2
| a15
| a ),
inference(copy,[status(thm)],[c_256]) ).
cnf(c_257,plain,
( ~ cI
| a
| s2
| a ),
inference(resolve,[status(thm)],[c_146,c_126]) ).
cnf(c_147,plain,
( ~ cI
| s2
| a ),
inference(copy,[status(thm)],[c_257]) ).
cnf(c_258,plain,
( a
| s2
| a ),
inference(resolve,[status(thm)],[c_147,c_140]) ).
cnf(c_149,plain,
( s2
| a ),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_151,plain,
( ~ a21
| ~ cI
| a ),
inference(resolve,[status(thm)],[c_149,c_49]) ).
cnf(c_259,plain,
( a
| ~ cI
| a ),
inference(resolve,[status(thm)],[c_151,c_124]) ).
cnf(c_152,plain,
( ~ cI
| a ),
inference(copy,[status(thm)],[c_259]) ).
cnf(c_260,plain,
( a
| a ),
inference(resolve,[status(thm)],[c_152,c_140]) ).
cnf(c_153,plain,
a,
inference(copy,[status(thm)],[c_260]) ).
cnf(c_154,plain,
( b
| a14 ),
inference(resolve,[status(thm)],[c_153,c_75]) ).
cnf(c_156,plain,
( ~ b
| a25 ),
inference(resolve,[status(thm)],[c_153,c_42]) ).
cnf(c_157,plain,
a23,
inference(resolve,[status(thm)],[c_153,c_35]) ).
cnf(c_158,plain,
( ~ b
| ~ a21 ),
inference(resolve,[status(thm)],[c_153,c_31]) ).
cnf(c_159,plain,
( b
| a21 ),
inference(resolve,[status(thm)],[c_153,c_29]) ).
cnf(c_161,plain,
( ~ b
| ~ a11 ),
inference(resolve,[status(thm)],[c_153,c_3]) ).
cnf(c_162,plain,
( ~ cI
| a22 ),
inference(resolve,[status(thm)],[c_157,c_34]) ).
cnf(c_163,plain,
( ~ a15
| s1
| b ),
inference(resolve,[status(thm)],[c_154,c_66]) ).
cnf(c_164,plain,
( ~ cI
| ~ a15
| b ),
inference(resolve,[status(thm)],[c_154,c_15]) ).
cnf(c_165,plain,
( cI
| s2
| b ),
inference(resolve,[status(thm)],[c_159,c_46]) ).
cnf(c_166,plain,
( cI
| s1
| b ),
inference(resolve,[status(thm)],[c_163,c_14]) ).
cnf(c_167,plain,
( ~ s2
| c2
| c1
| cI
| b ),
inference(resolve,[status(thm)],[c_166,c_85]) ).
cnf(c_261,plain,
( cI
| b
| c2
| c1
| cI
| b ),
inference(resolve,[status(thm)],[c_167,c_165]) ).
cnf(c_262,plain,
( cI
| c2
| c1
| cI
| b ),
inference(copy,[status(thm)],[c_261]) ).
cnf(c_168,plain,
( c2
| c1
| cI
| b ),
inference(copy,[status(thm)],[c_262]) ).
cnf(c_170,plain,
( ~ a11
| ~ a15
| c2
| cI
| b ),
inference(resolve,[status(thm)],[c_168,c_27]) ).
cnf(c_263,plain,
( cI
| ~ a11
| c2
| cI
| b ),
inference(resolve,[status(thm)],[c_170,c_14]) ).
cnf(c_171,plain,
( ~ a11
| c2
| cI
| b ),
inference(copy,[status(thm)],[c_263]) ).
cnf(c_264,plain,
( b
| c2
| cI
| b ),
inference(resolve,[status(thm)],[c_171,c_2]) ).
cnf(c_172,plain,
( c2
| cI
| b ),
inference(copy,[status(thm)],[c_264]) ).
cnf(c_174,plain,
( a26
| a22
| cI
| b ),
inference(resolve,[status(thm)],[c_172,c_52]) ).
cnf(c_175,plain,
( a25
| a22
| cI
| b ),
inference(resolve,[status(thm)],[c_174,c_44]) ).
cnf(c_265,plain,
( b
| a22
| cI
| b ),
inference(resolve,[status(thm)],[c_175,c_41]) ).
cnf(c_176,plain,
( a22
| cI
| b ),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_266,plain,
( cI
| cI
| b ),
inference(resolve,[status(thm)],[c_176,c_32]) ).
cnf(c_177,plain,
( cI
| b ),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_178,plain,
( a22
| b ),
inference(resolve,[status(thm)],[c_177,c_162]) ).
cnf(c_179,plain,
( c2
| b ),
inference(resolve,[status(thm)],[c_178,c_50]) ).
cnf(c_180,plain,
( a15
| conjline18
| b ),
inference(resolve,[status(thm)],[c_179,c_84]) ).
cnf(c_182,plain,
( s2
| s1
| a15
| b ),
inference(resolve,[status(thm)],[c_180,c_55]) ).
cnf(c_267,plain,
( a15
| s2
| a15
| b ),
inference(resolve,[status(thm)],[c_182,c_82]) ).
cnf(c_183,plain,
( s2
| a15
| b ),
inference(copy,[status(thm)],[c_267]) ).
cnf(c_268,plain,
( ~ cI
| b
| s2
| b ),
inference(resolve,[status(thm)],[c_183,c_164]) ).
cnf(c_184,plain,
( ~ cI
| s2
| b ),
inference(copy,[status(thm)],[c_268]) ).
cnf(c_269,plain,
( b
| s2
| b ),
inference(resolve,[status(thm)],[c_184,c_177]) ).
cnf(c_186,plain,
( s2
| b ),
inference(copy,[status(thm)],[c_269]) ).
cnf(c_188,plain,
( ~ a21
| ~ cI
| b ),
inference(resolve,[status(thm)],[c_186,c_49]) ).
cnf(c_270,plain,
( b
| ~ cI
| b ),
inference(resolve,[status(thm)],[c_188,c_159]) ).
cnf(c_189,plain,
( ~ cI
| b ),
inference(copy,[status(thm)],[c_270]) ).
cnf(c_271,plain,
( b
| b ),
inference(resolve,[status(thm)],[c_189,c_177]) ).
cnf(c_190,plain,
b,
inference(copy,[status(thm)],[c_271]) ).
cnf(c_191,plain,
~ a11,
inference(resolve,[status(thm)],[c_190,c_161]) ).
cnf(c_192,plain,
~ a21,
inference(resolve,[status(thm)],[c_190,c_158]) ).
cnf(c_193,plain,
a25,
inference(resolve,[status(thm)],[c_190,c_156]) ).
cnf(c_194,plain,
( ~ c2
| conjline18 ),
inference(resolve,[status(thm)],[c_191,c_83]) ).
cnf(c_195,plain,
( ~ cI
| s1 ),
inference(resolve,[status(thm)],[c_191,c_80]) ).
cnf(c_197,plain,
~ a14,
inference(resolve,[status(thm)],[c_191,c_77]) ).
cnf(c_202,plain,
( cI
| ~ s2 ),
inference(resolve,[status(thm)],[c_192,c_48]) ).
cnf(c_203,plain,
( ~ cI
| s2 ),
inference(resolve,[status(thm)],[c_192,c_47]) ).
cnf(c_204,plain,
( cI
| a26 ),
inference(resolve,[status(thm)],[c_193,c_70]) ).
cnf(c_207,plain,
( cI
| ~ s1 ),
inference(resolve,[status(thm)],[c_197,c_81]) ).
cnf(c_211,plain,
( c2
| cI ),
inference(resolve,[status(thm)],[c_204,c_51]) ).
cnf(c_212,plain,
( conjline18
| cI ),
inference(resolve,[status(thm)],[c_211,c_194]) ).
cnf(c_213,plain,
( s2
| s1
| cI ),
inference(resolve,[status(thm)],[c_212,c_55]) ).
cnf(c_272,plain,
( cI
| s2
| cI ),
inference(resolve,[status(thm)],[c_213,c_207]) ).
cnf(c_214,plain,
( s2
| cI ),
inference(copy,[status(thm)],[c_272]) ).
cnf(c_273,plain,
( cI
| cI ),
inference(resolve,[status(thm)],[c_214,c_202]) ).
cnf(c_215,plain,
cI,
inference(copy,[status(thm)],[c_273]) ).
cnf(c_217,plain,
s2,
inference(resolve,[status(thm)],[c_215,c_203]) ).
cnf(c_218,plain,
s1,
inference(resolve,[status(thm)],[c_215,c_195]) ).
cnf(c_219,plain,
a22,
inference(resolve,[status(thm)],[c_215,c_162]) ).
cnf(c_274,plain,
( ~ s2
| ~ conjline18 ),
inference(resolve,[status(thm)],[c_218,c_56]) ).
cnf(c_221,plain,
~ conjline18,
inference(resolve,[status(thm)],[c_217,c_274]) ).
cnf(c_222,plain,
c2,
inference(resolve,[status(thm)],[c_219,c_50]) ).
cnf(c_275,plain,
~ c2,
inference(resolve,[status(thm)],[c_221,c_194]) ).
cnf(c_224,plain,
$false,
inference(resolve,[status(thm)],[c_222,c_275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV003-3 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:59:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3297564 was started by sandbox on n006,
% 0.10/0.37 % Fri Sep 25 15:59:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 182.
% 0.10/0.40 % Level of proof is 79.
% 0.10/0.40 % Maximum clause weight is 7.000.
% 0.10/0.40 % Given clauses 209.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------